The top court has asked both the Central government and the RBI to address the issue within two weeks.
A bench of Chief Justice J S Khehar and Justice D Y Chandrachud asked Solicitor General Ranjit Kumar, appearing for the Central government, to take instructions on the issue and inform the court.
Ranjit Kumar sought time to get instructions for granting an opportunity to people to deposit their money on a case-by-case basis.
The bench said there are people who could not deposit their old currency note during the December 30 deadline - like those in prison.
"We want to know as to why you chose to bar such persons," it asked.
The court was hearing a batch of petitions, including a woman who said she had just delivered a baby and another who said she was dealing with a death in her family.
The pleas sought direction to authorities to allow them to deposit demonetised notes.
On November 8, 2016, the Central government had announced that Rs 500 and Rs 1,000 notes would no longer be legal tender from November 9.
The government had assured the people that demonetised currency notes could be exchanged at banks, post offices and RBI branches till December 30, 2016. If people were unable to deposit them by that day, they could do so till March 31, 2017 at RBI branches after complying with certain formalities.